Transportation Problems

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Transportation Assignment and Transshipments Problems
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Transportation Problems Decision making and Organization Management Transportation Problems Pongsa Pornchaiwiseskul Faculty of Economics Chulalongkorn University Pongsa Pornchaiwiseskul, Faculty of Economics, Chulalongkorn University Pongsa Pornchaiwiseskul, Faculty of Economics, Chulalongkorn University

Drug Distribution Drugco has three drug factories that supply the need for four provinces. Each drug factory can supply the following numbers of tons of drug per month: factory A, 35; factory B, 50; factory C, 40. The drug demands in these provinces are as follows (in tons per month): province 1, 45; province 2, 20; province 3, 30; province 4, 30. The costs of distribution from factory to province depend on the distance as given in table below. Pongsa Pornchaiwiseskul, Faculty of Economics, Chulalongkorn University

Pongsa Pornchaiwiseskul, Faculty of Economics, Chulalongkorn University

Graphical Representation Factory Province 1 45 35 A 2 20 50 B 3 30 40 C 4 30 Pongsa Pornchaiwiseskul, Faculty of Economics, Chulalongkorn University

LP Formulation Define xij = tons/month of drug shipped from factory i to province j i = A, B, C j = 1, 2, 3, 4 Pongsa Pornchaiwiseskul, Faculty of Economics, Chulalongkorn University

LP Problem for Balanced Transportation Problem MIN 8xA1+ 6xA2+ 10xA3+ 9xA4 + 9xB1+ 12xB2+ 13xB3+ 7xB4 + 14xC1+ 9xC2+ 16xc3+ 5xC4 subject to xA1+ xA2+ xA3+ xA4 = 35 xB1+ xB2+ xB3+ xB4 = 50 xC1+ xC2+ xc3+ xC4 = 40 Pongsa Pornchaiwiseskul, Faculty of Economics, Chulalongkorn University

LP Problem (cont’d) for Balanced Transportation Problem xA1+ xB1+ xC1 = 45 xA2+ xB2+ xC2 = 20 xA3+ xB3+ xC3 = 30 xA4+ xB4+ xC4 = 30 xij >= 0 for all i,j Pongsa Pornchaiwiseskul, Faculty of Economics, Chulalongkorn University

LINDO inputs for Balanced Transportation Problem min 8xa1+6xa2+10xa3+9xa4 +9xb1+12xb2+13xb3+7xb4 +14xc1+9xc2+16xc3+5xc4 subject to 2) xa1+xa2+xa3+xa4=35 3) xb1+xb2+xb3+xb4=50 4) xc1+xc2+xc3+xc4=40 Pongsa Pornchaiwiseskul, Faculty of Economics, Chulalongkorn University

LINDO inputs (cont’d) for Balanced Transportation Problem 5) xa1+xb1+xc1=45 6) xa2+xb2+xc2=20 7) xa3+xb3+xc3=30 Pongsa Pornchaiwiseskul, Faculty of Economics, Chulalongkorn University

TABLEAU Method Pongsa Pornchaiwiseskul, Faculty of Economics, Chulalongkorn University

TABLEAU Method Pongsa Pornchaiwiseskul, Faculty of Economics, Chulalongkorn University

TABLEAU Method Pongsa Pornchaiwiseskul, Faculty of Economics, Chulalongkorn University

TABLEAU Method Pongsa Pornchaiwiseskul, Faculty of Economics, Chulalongkorn University

TABLEAU Method Pongsa Pornchaiwiseskul, Faculty of Economics, Chulalongkorn University

TABLEAU Method Pongsa Pornchaiwiseskul, Faculty of Economics, Chulalongkorn University

TABLEAU Method Pongsa Pornchaiwiseskul, Faculty of Economics, Chulalongkorn University

TABLEAU Method Pongsa Pornchaiwiseskul, Faculty of Economics, Chulalongkorn University

TABLEAU Method Pongsa Pornchaiwiseskul, Faculty of Economics, Chulalongkorn University

TABLEAU Method Pongsa Pornchaiwiseskul, Faculty of Economics, Chulalongkorn University

TABLEAU Method Pongsa Pornchaiwiseskul, Faculty of Economics, Chulalongkorn University

Unbalanced Transportation Problem Pongsa Pornchaiwiseskul, Faculty of Economics, Chulalongkorn University

LP Problem for Unbalanced Transportation Problem Min 8xA1+ 6xA2+ 10xA3+ 9xA4 + 9xB1+ 12xB2+ 13xB3+ 7xB4 + 14xC1+ 9xC2+ 16xc3+ 5xC4 subject to xA1+ xA2+ xA3+ xA4 +dA= 45 xB1+ xB2+ xB3+ xB4 +dB = 50 xC1+ xC2+ xc3+ xC4 +dC = 40 Pongsa Pornchaiwiseskul, Faculty of Economics, Chulalongkorn University

LP Problem (cont’d) for UnBalanced Transportation Problem xA1+ xB1+ xC1 = 45 xA2+ xB2+ xC2 = 20 xA3+ xB3+ xC3 = 30 xA4+ xB4+ xC4 = 30 xij ,di>= 0 for all i,j Pongsa Pornchaiwiseskul, Faculty of Economics, Chulalongkorn University

Unbalanced Transportation Problem Pongsa Pornchaiwiseskul, Faculty of Economics, Chulalongkorn University

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